Wave guide taper



June 19, 1962 E. A. OHM

WAVE GUIDE TAPER Filed May 27. 1959.

TERMINAL CROSS SECTIONS ALUMINUM MANDREL REF INVENTOR E. A OHM 7. VJ A Tram/K /N FIG. 44 L CON/CA1. SURFACE United States Patent Ofifice 3,040,277 Patented June 19, 1962 3,040,277 WAVE GUIDE TAPER Edward A. Ohm, Shrewsbury, N.J., assignor to Bell Telephone Laboratories, Incorporated, New York, N.Y., a corporation of New York Filed May 27, 1959, Ser. No. 816,0?8 3 Claims. (Cl. 333-34) This invention relates to electromagnetic wave transmission systems for use in the high, microwave, and millimeter Wave frequency ranges, and more particularly to wave guide transition tapers for use in such systems.

Frequently in wave guide system practice, it becomes necessary to join successive Wave guide sections which differ in physical and/or electrical properties. A substantial portion of the prior art in this area is concerned with the case of joining guides of widely differing characteristic impedances within a minimum of energy reflection. The well-known quarter wave impedance transformer, the Gaussian impedance taper, the exponential impedance taper, and the 'Ischebyscheif impedance taper are copiously treated in the published art. It frequently becomes desirable to join successive wave guide sections which have characteristic impedances which are similar but transverse cross-sectional shapes which are dissimilar. In much of the prior work dealing with impedance transforming transition sections, the distributed shunt susceptance associated with the particular transition involved has been assumed to be zero or, at least, negligible in view of the large impedance differential. When, however, the impedances of the sections to be joined are identical or nearly so, the distributed shunt susceptance becomes the major cause of the reflection from the transition.

It is, therefore, a major object of this invention to join successive wave guide sections having dissimilar transverse cross-sectional shapes.

It is a further object of this invention to join successive wave guide sections having similar characteristic impedances and dissimilar transverse cross-sectional shapes by means producing very low energy reflection.

It is a. more specific object of the invention to join these successive guide sections by a wave guide transition section characterized by low distributed shunt susceptance.

Generally, the reflection characteristics of a wave guide transition taper may be minimized by selecting a section having a long length. However, long transitions are preferably to be avoided to conserve space.

A feature of the present invention is its over-all length, which may be of the order of three-quarters of a guide wavelength at the operating frequency.

In accordance with the principal embodiment of the invention, the guides to be joined are of circular and square transverse cross-section, respectively, and the transition section takes the form of a smooth reference taper. The surface contour of the taper comprises successive transverse cross-sections each of which is itself described by a set of four successive arcs struck through four determinable sets of three points each. in order to determine these points, and thus the over-all contour of the novel guide transition, the corners and centers of the rectangle sides are connected to octant points on the circle, selecting whatever impedance taper program is desired for these lines. Then, along each set of three lines (corresponding to the four sides of the rectangle locus) at locations on each line which are the same proportional part of the total length of this line, the only circular are which will join each set of points is struck. Proceeding in thi manner at successive locations from the rectangular guide to the circular guide results in a transition section, designated a smooth reference taper, in accordance with the invention.

A feature of the invention resides in the use of simple polyfoam tuning elements to eliminate the small shunt susceptance which remains.

The above and other objects and features of the invention will become more clearly understood by reference to the accompanying drawing in which:

FIG. 1 is a perspective view of a guide transition in accordance with the invention;

FIG. 2, given by way of explanation, is a pictorial representation helpful in visualizing the procedure leading to the transition of FIG. 1;

FIG. 3 is a perspective view of a shaped mandrel for use in a practical method of fabrication of the invention;

FIG. 4 illustrates a tuning element useful in conjunction with the invention;

FIG. 4A is a vector diagram related to the element shown in FIG. 4; and

FIG. 5 is a perspective view of an alternate transition section geometry.

Referring more particularly to the drawing, FIG. 1 illustrates a hollow conductively bounded wave guide section 10 of circular transverse cr0ss-section of radius r joined through a smooth reference taper 11 in accordance with the invention to a hollow conductively bounded 'wave guide section 12 of rectangular transverse cross- 'istic impedance and while this quantity may be defined in several different ways, each appropriate for its own purposes, in this specification the term characteristic impedance shall be understood to be the ratio of the square of the R.M.S. voltage along the electric field line where the electric field is a maximum to the total power flowing when the guide is match-terminated. This irnpedance convention is referred to as that of power and voltage.

While the invention is applicable to any of the large variety of wave mode configurations ordinarily sup ported by hollow pipe guides, the specific description of the invention herein will be confined to the case of transverse electric, or TE waves by way of simplification.

The impedance of guide section 10, when air-filled is Fidel ohms where r is the radius and 7t the wavelength of interest. 7

ohms

where a and b are the transverse cross-sectional dimen sions of the guide.

It is readily apparent from the above equations that l the characteristic impedance of a circular pipe may vary from infinity at the cut-off wavelength to 764ohms for infinitely large pipes, whereas the characteristic impedance of the rectangular pipe may be varied from infinity at cut-ofl to zero; Thus the impedance of a rectangular guide may be made equal to that of a given circular guide merely by proportioning the dimensions a and b of the rectangular guide.

As disclosed in my copending application, Serial No.

724,684, filed March 28, 1958, now U.S.'Patent 2,972,-

applications require a transition between circular guides and square guides as well as between circular guides and near-square guides, both with an input polarization inclined at 45 degrees to thewalls of the rectangular guide. In such'a-case it.is necessary thatthe impedances seen by the vertically polarized component and-the horizontally,polarizedcomponent be as nearly equalas possible. For the square guide no problem ispresented but forthe near-square guide these impedancescan never be exactly equal. However, as disclosed in the above copending application, applicant has .found that.the.effective differ-. ence inthe characteristic impedances presented to the orthogonal components ofthe 45-degree inputpolarization is .zeroif the impedance of the circularguide is made equal to the square root of the product of the impedances presented by the near-square guide to the two polarization components.

Itbecomes clear, therefore, ,thatthe transition taper to,

be described below has wide. application to the problem of joining round and rectangular wave guides andisnot limited to any single combination of guides, their characteristic impedances, wave energy polarizations, and wave modes. More particularly, when the direction of polarization of the input waves is normal to one pair of walls of the rectangular guide, it is not necessary that any equality of impedances exist between the round and rectangular guides;

Returning now toFIG. 1, the transition taper 11, or smooth reference taper, isahollow conductively bounded wave guide element which preserves the impedance equal-v ity between guides 10 and 12 while providing .a' transition of'transversecross section from round to rectangular with very, lowattendant reflection-of wave energy. The taper is characterized by smoothness of'physicalcontour, successive=cross sections-being only slightly different from eaclbother. The precise shape assumed by taper-11 may be more readily understood by reference to FIG. 2. In

FIG. 2 theterminal transverse crosssections-of. guides 19 and 1-2 to be joined are symmetrically superimposed as circle locus 20'and rectangle locus 2.1. Since the surface contour of taper 11 may be broken down into four identical quarters, the method'of synthesizing only. one of these quarters will be set out, the remainder of the process being. a matter of course once one side is known. In FIG. 2 the derivation ofa typicalcross section curvature sector for the upper poltion of the smooth reference taper surface is set out. Points 0, d, e, corresponding to the ends and center of the top of 'the rectangle locus 21, are connected by'means of lines 22, 23, and24, respectively,

to points c, d, and e, respectively, on the circle locus 20. Points c, d, and e are octantpoints on the circle; i.e., they are each separated by an arc of circle 21 which subtends an angle of 45 degrees at the circles center.

Each oflines.cc, dd, and ee' is programmed; i.e.,

poses l of illustration in. this: application, but. no limitation is to be deduced therefrom. Thus, in FIG. 2 .lines'cc', d+d' and e-e are straightilines. To determine any given surface contour, points C,.D, and 'E are located on lines cc, al -d, andie-e', respectively, at distances from the rectangle locus on each line which bears the.

same proportionality to Thus in FIG. 2;

the totalv length of that line.

Through the set of three points thus determined are 25 is struck. This are represents the surface contour of a smooth reference taper at the transverse cross section of which it is a part. Geometrically are 25 may always be struck by first locating point 26 by extending the perpendicular bisectors of lines joining CD and DE until they intersect. Once point 26 is established the radius R is known. By repeating the above procedure four times at a given cross section, the complete surface contour at any given transverse cross section of a smooth reference taper may be determined. It may readily be seen from FIG. 1 that, as the rectangle locus 21 is approached along the taper section, radius R will increase and finally reach infinity at the rectangular terminal cross section. Likewise, as the circle locus is approached, R will approach I", the radius of the terminal cross section 20. The respective points mentioned above with reference to FIG. 2 have been set out in FIG. 1, together with are 25 for purposes of visualization.

FIG. 3 is a perspective view of a mandrel and spacers which may be used in the fabrication of a smooth reference taper transition in accordance with the invention. The problems of fabrication are not so great as might first appear from a consideration of the procedure set out above. One method whereby the smooth reference taper may be constructed involvesthe use of a mandrel 39 which may be of aluminum or other suitable material and over which a smooth reference taper may be electroforrned in accordance with well-known techniques.

Mandrel 3% can be rough-shaped by milling all the radii, shown typically as R in FIG. 2, for equally spaced cross sections by using a series of end mounted templates. To avoid removing material necessary for smooth surface tapering, the cutter axismay be tilted slightly toward the round wave guide axis. The excess material can then be removed, for example by filing, to join the accurate cuts smoothly.. -t often occurs that the relative dimensions of the terminal cross sections are such that the mandrel cannot be pulledF from the electroformed component in the conventional manner. For example, as seen'in FIG. 2, the circle locus 2t exceeds the dimensions of the rectangle locus 21 at some locations while the reverse is true at other'locations. Therefore, to provide for non-destructive mandrel removal, the taper transition may beelectroformedin top and bottom halves by inserting dielectric spacers 31 which may comprise polystyrene, for example, asshown in FIG. 3. After the mandrel is removed the top and bottom halves may be conductively joined by soldering-metallic spacers of thickness identical to that of the dielectric spacers between the halves.

As stated hereinabove, .a smooth reference taper in accordance with the present invention is characterized by a. very low. reflection coefiicient. For some applications, however, it is desirable that the reflection coefficient be reduced even further. FIG. 4 illustrates a tuning element 46 which may be advantageously used for tuning purposes. The material of the element may be polyfoam or some other dielectric depending on the magnitude of the reflection to be canceled. In the smooth reference taper the reflection level is very low and a very low dielectric constant material is desirable. Tuning element 45 functions in some respects like a conventional metallic tuning screw. However, in at least its multimoding characteristics, the tuning wedge is superior. to the tuning screw. Element 4%} is physically simple, comprising an element of dielectric material in the shape of an isosceles triangle. The height h of element 40, which determines the reflection coefficient of the element, is determined first and the length of sloping sides 41', 4-2 is then chosen such'that the midpoints of the'sloping sides are spaced one-quarter guide wavelength at the frequency to be affected. If the midpoint of the element 40 be taken as the reference plane for an incident wave E the local resistive reflec-v tions it to (-n), indicated by vectors 43 in FIG. 4 add vectorially to produce an over-all reflection which lags the input by '90 degrees as may be seen from the vector diagram ofFIG. 4A. By placing the center line ofelernent 40 ninety electrical degrees beyond the center line of a smooth reference taper section, the reflections due to the taper and the reflections due to the tuning wedge cancel. A very high quality transition section between the guides to be joined results.

For certain applications it has been found desirable to utilize four tuning triangles spaced ninety physical degrees apart around the inside surface of the transition taper. When the guide system of which the taper is a. part is adapted to support a broad frequency band, the guide will inherently support many wave modes at the higher frequencies. The triangular tuning wedge causes virtually no multimoding at the higher frequencies while at the same time effectively tuning out the reflections at the lower frequencies in which range they are most severe.

FIG. 5 illustrates a transition taper which may be used as an alternate to the smooth reference taper shown in FIG. 1. In FIG. 5 the rectangular terminal cross section 50 to be joined is circumscribed by a circle 51 and the circle is connected through conical surface 52 to the circle 53 formed by the terminal aperture of the round guide to be joined. Successive planar slices of this conical surface are then taken, joining the sides of the rectangle with quadrant points on the circle. The resulting sliced conical taper transition is characterized by low distributed shunt susceptance and attendant reflections. The dielectric tuning element of FIG. 4 may be used with the sliced conical taper to tune out residual reflections in the same manner as it was used with the smooth reference taper.

In all cases it is understood that the above-described arrangements are illustrative of a small number of the many specific embodiments which could represent an application of the principle of the invention. Other arrangements, including transition tapers between guides of transverse cross sectional shapes other than those illustrated and characteristic impedances other than those described, could readily be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention.

What is claimed is:

1. In combination, a bounded wave guide section adapted to support electromagnetic wave energy, over a given band of frequencies, said section having a first terminal end of a first transverse cross sectional geometry and a second terminal end of a second transverse cross sectional geometry diflerent from said first cross sectional geometry, the surface of said section between said terminal ends conforming to eight predetermined lines between respective spaced points on each of said terminal ends, the transverse cross sectional geometry of said section being described by circular arcs through points along sets of three of said lines, said arcs having radii which vary at succesive cross sections from said first terminal end to said second terminal end, said points being the same proportionate distances along each line of said sets from a given terminal end, and means for eliminating reflections due to the distributed shunt susceptance of said transition section disposed within said section intermediate the ends thereof, said means comprising at least one dielectric element having a dielectric constant different from the dielectric constant of the medium filling the remainder of said transition section, said dielectric element having a longitudinal cross section in the shape of an isosceles triangle and having a rectangular transverse cross section with midpoints of the equal sides of said triangular cross section spaced apart a distance equal to one quarter wavelength at the midfrequency of said band of frequencies.

2. The combination according to claim 1 wherein said means comprises four identical dielectric elements sym metrically disposed around the inside surface of said transition section and in the same transverse plane.

3. The combination according to claim 1 wherein the longitudinal center of said dielectric element is spaced from the transverse plane defining the center of said transition section a distance equal to one quarter wavelength at the midfrequency of said band of frequencies.

References Cited in the file of this patent UNITED STATES PATENTS 2,566,377 Robertson June 12, 1951 2,742,612 Cohn Apr. 17, 1956 2,878,453 Elliott Mar. 17, 1959 2,881,399 Leyton Apr. 7, 1959 FOREIGN PATENTS 711,807 Great Britain July 14, 1954- 65,'027 France Sept. 21, 1955 

